Solve for $x$ and $y$ using elimination. ${-x+6y = 33}$ ${4x+5y = 42}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ ${-4x+24y = 132}$ $4x+5y = 42$ Add the top and bottom equations together. $29y = 174$ $\dfrac{29y}{{29}} = \dfrac{174}{{29}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x+6y = 33}\thinspace$ to find $x$ ${-x + 6}{(6)}{= 33}$ $-x+36 = 33$ $-x+36{-36} = 33{-36}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 6}$ into $\thinspace {4x+5y = 42}\thinspace$ and get the same answer for $x$ : ${4x + 5}{(6)}{= 42}$ ${x = 3}$